Abstract

On a finite time horizon, we consider a control system described by a vector differential equation with right-hand side that changes its structure at some times spaced by a distance that cannot be less than a certain given value. In between two adjacent structure change instants, the right-hand side is a function that is Lipschitz in state variables, continuous in time, and linear in the control and perturbation, which take values in some convex closed sets. It is assumed that at the structure change instants the solution of the system may experience a jump by a certain vector of which only the direction is known. A uniform mesh is specified on the system operation interval. The values of the state vector are measured (with an error) at the mesh points. We solve the problem of constructing an algorithm for the formation of a system control that ensures bringing the system trajectory to the minimum possible neighborhood of the goal set at the end time. A solution algorithm is indicated that is based on the constructions of positional control theory and is resistant to information interferences and computational errors.

中文翻译：

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右侧不连续系统的控制问题中的反馈

摘要

在有限的时间范围内，我们考虑用矢量微分方程描述的控制系统，该矢量控制方程的右手边有时会改变其结构，且其间隔不得小于某个给定值。在两个相邻的结构变化瞬间之间，右侧是一个函数，状态变量为Lipschitz，时间连续，并且在控制和扰动中呈线性，这些函数在某些凸封闭集中具有值。假设在结构变化的瞬间，系统的解可能会经历一定方向的跳跃，而方向仅是已知的。在系统操作间隔上指定了均匀的网格。在网格点处测量状态向量的值（有误差）。我们解决了构建用于形成系统控件的算法的问题，该算法可确保在结束时使系统轨迹达到目标设置的最小可能邻域。提出了一种基于位置控制理论的解决方案算法，该算法可抵抗信息干扰和计算错误。